Title: Theory of Open Quantum Systems and Quantum Thermodynamics

Convenor: Kay Brandner (Nottingham)

Commitment: 10 lectures x 1 hour, 2 lectures / week, online (Zoom)

Dates and times: Tuesdays and Fridays from 1:00 PM to 2:00 PM, start date 16th Jan 2024

Assessment: problem sheets, 1 / week, 50% overall score required to pass

Module Details:

The aim of this module is to provide general theoretical tools to describe the dynamics of open quantum systems. We develop a systematic approach to quantum master equations, which are widely used in quantum optics, quantum opto-mechanics, cold-atom, solid-state and statistical physics. We show how these master equations can be derived from microscopic models, discuss their range of validity, their consistency with the laws of thermodynamics and methods to solve them. In the last part of this module, we apply these methods to quantum thermal machines and discuss recent developments in this area. The module is primarily designed for post-graduate students working in theoretical condensed matter physics, but is open to anyone, who is interested in the topic. Solid background knowledge on quantum mechanics, statistical and thermal physics will be helpful to follow this module.

Specific topics include:

(I) Mathematical basics of the theory of open quantum systems (dynamical maps, complete positivity,
GKSL (Lindblad) equations).

(II) Microscopic derivations of quantum master equations (Nakajima-Zwanzig formalism, weak-coupling theory for free and driven systems, Born-Markov approximation).

(III) Methods to solve quantum master equations (exact methods, simulation methods, perturbation theory).

(IV) Thermodynamics of open quantum systems (detailed balance, the first and the second law, thermodynamic consistency of quantum master equations).